@inproceedings{4f4ef6ffc7c54f739c7065925e50242c,
title = "Covering many or few points with unit disks",
abstract = "Let P be a set of n weighted points. We study approximation algorithms for the following two continuous facility-location problems. In the first problem we want to place m unit disks, for a given constant m=1, such that the total weight of the points from P inside the union of the disks is maximized. We present a deterministic algorithm that can compute, for any e>0, a (1-e)-approximation to the optimal solution in O(n logn + e-4mlog2m (1/e)) time. In the second problem we want to place a single disk with center in a given constant-complexity region X such that the total weight of the points from P inside the disk is minimized. Here we present an algorithm that can compute, for any e>0, with high probability a (1+e)-approximation to the optimal solution in O(n (log3 n + e-4 log2 n )) expected time.",
author = "{Berg, de}, M. and S. Cabello and S. Har-Peled",
year = "2007",
doi = "10.1007/11970125_5",
language = "English",
isbn = "978-3-540-69513-4",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "55--68",
editor = "T. Erlebach and C. Kaklamanis",
booktitle = "Proceedings of the 4th International Workshop on Approximation and Online Algorithms (WAOA 2006) 14-15 September 2006, Z{\"u}rich, Switzerland",
address = "Germany",
note = "conference; WAOA 2006, Zurich, Switzerland; 2006-09-14; 2006-09-15 ; Conference date: 14-09-2006 Through 15-09-2006",
}